Oyama Norihiro, Mizuno Hideyuki, Ikeda Atsushi
Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Tokyo 153-8902, Japan.
Mathematics for Advanced Materials-OIL, AIST, Sendai 980-8577, Japan.
Phys Rev E. 2021 Jul;104(1-2):015002. doi: 10.1103/PhysRevE.104.015002.
Plastic events in sheared glasses are considered an example of so-called avalanches, whose sizes obey a power-law probability distribution with the avalanche critical exponent τ. Although the so-called mean-field depinning (MFD) theory predicts a universal value of this exponent, τ_{MFD}=1.5, such a simplification is now known to connote qualitative disagreement with realistic systems. Numerically and experimentally, different values of τ have been reported depending on the literature. Moreover, in the elastic regime, it has been noted that the critical exponent can be different from that in the steady state, and even criticality itself is a matter of debate. Because these confusingly varying results have been reported under different setups, our knowledge of avalanche criticality in sheared glasses is greatly limited. To gain a unified understanding, in this work, we conduct a comprehensive numerical investigation of avalanches in Lennard-Jones glasses under athermal quasistatic shear. In particular, by excluding the ambiguity and arbitrariness that has crept into the conventional measurement schemes, we achieve high-precision measurement and demonstrate that the exponent τ in the steady state follows the prediction of MFD theory, τ_{MFD}=1.5. Our results also suggest that there are two qualitatively different avalanche events. This binariness leads to the nonuniversal behavior of the avalanche size distribution and is likely to be the cause of the varying values of τ reported thus far. To investigate the dependence of criticality and universality on applied shear, we further study the statistics of avalanches in the elastic regime and the ensemble of the first avalanche event in different samples, which provide information about the unperturbed system. We show that while the unperturbed system is indeed off-critical, criticality gradually develops as shear is applied. The degree of criticality is encoded in the fractal dimension of the avalanches, which starts from zero in the off-critical unperturbed state and saturates in the steady state. Moreover, the critical exponent τ is consistent with the prediction of the MFD τ_{MFD} universally, regardless of the amount of applied shear, once the system becomes critical.
剪切玻璃中的塑性事件被认为是所谓雪崩的一个例子，其大小服从具有雪崩临界指数τ的幂律概率分布。尽管所谓的平均场脱钉（MFD）理论预测了该指数的一个通用值，即τMFD = 1.5，但现在已知这种简化意味着与实际系统存在定性分歧。在数值和实验方面，根据文献报道，τ有不同的值。此外，在弹性区域，人们已经注意到临界指数可能与稳态时的不同，甚至临界性本身也是一个有争议的问题。由于在不同设置下报道了这些令人困惑的不同结果，我们对剪切玻璃中雪崩临界性的了解非常有限。为了获得统一的理解，在这项工作中，我们对Lennard-Jones玻璃在无热准静态剪切下的雪崩进行了全面的数值研究。特别是，通过排除传统测量方案中出现的模糊性和任意性，我们实现了高精度测量，并证明稳态下的指数τ遵循MFD理论的预测，即τMFD = 1.5。我们的结果还表明存在两种定性不同的雪崩事件。这种二元性导致了雪崩大小分布的非通用行为，并且很可能是迄今为止报道的τ值变化的原因。为了研究临界性和通用性对施加剪切的依赖性，我们进一步研究了弹性区域中的雪崩统计以及不同样品中第一个雪崩事件的系综，这提供了关于未受扰动系统的信息。我们表明，虽然未受扰动的系统确实是非临界的，但随着剪切的施加临界性会逐渐发展。临界程度编码在雪崩的分形维数中，它在非临界未受扰动状态下从零开始，在稳态下达到饱和。此外，一旦系统变得临界，临界指数τ普遍与MFD的预测τMFD一致, 而与施加的剪切量无关。
